• DOI:10.3842/SIGMA.2015.053
• Corpus ID: 17029867

Constructing Involutive Tableaux with Guillemin Normal Form

@article{Smith2014ConstructingIT,
  title={Constructing Involutive Tableaux with Guillemin Normal Form},
  author={Abraham Smith},
  journal={Symmetry Integrability and Geometry-methods and Applications},
  year={2014},
  volume={11},
  pages={053}
}

• Abraham Smith
• Published 28 October 2014
• Mathematics
• Symmetry Integrability and Geometry-methods and Applications

Involutivity is the algebraic property that guarantees solutions to an analytic and torsion-free exterior differential system or partial differential equation via the Cartan{Kahler theorem. Guillemin normal form establishes that the prolonged symbol of an involutive system admits a commutativity property on certain subspaces of the prolonged tableau. This article examines Guillemin normal form in detail, aiming at a more systematic approach to classifying involutive systems. The main result is an explicit quadratic condition for involutivity of the type suggested but not completed in Chapter IV,x 5 of the book Exterior Dierential Systems by Bryant, Chern, Gardner, Goldschmidt, and Griffiths. This condition enhances Guillemin normal form and characterizes involutive tableaux.